1. Field of the Invention
This invention relates to a scanning force microscope operating in an AC mode, and, more particularly, to an automatic surface engagement feature for such a microscope, and to amplitude demodulation apparatus for such a microscope.
2. Background Information
Typically, a non-contact or cyclic-contact scanning force microscope is operated in an AC detection mode, with a cantilever having a probe tip at its distal end being vibrated at or near its resonance frequency, and with the amplitude of vibration of the probe tip being detected by one of a variety of methods. When the tip is brought into proximity with the sample surface, its vibration amplitude becomes a function of interactions between the tip and the sample surface. In non-contact scanning force microscopy, a long-range interaction force gradient alters the resonance characteristics of the cantilever, resulting in variation of the amplitude of vibration. In cyclic-contact scanning force microscopy, a short-range repulsive interaction between the tip and the sample surface dampens the vibration of the cantilever, reducing the amplitude of tip vibration. Therefore, when the amplitude of vibration is regulated as the probe is scanned across the sample surface, a servo control loop is provided to maintain the separation between the tip and the sample surface at a constant level, allowing a map showing properties of the surface to be made.
The optimization of parameters, such as the frequency of vibration, controlling AC-mode scanning force microscopy is critical for obtaining accurate measurements. In a non-contact AC mode, in order to obtain a highly sensitive servo control, the vibration frequency is preferably operated at a value for which the slope of a resonance curve, indicating amplitude as a function of frequency, is greatest. It is further desirable to engage the tip to the surface as closely as possible without contacting the surface. In a cyclic-contact mode, the engagement of the tip with the sample surface is controlled to avoid significant wear of the tip or damage to the sample being measured.
In the non-contact AC mode, before the tip engages the sample surface, the frequency of operation is set at the value corresponding to a steepest point of the resonance curve. However, as the tip approaches the sample surface, the increasing force gradient alters the resonance properties, shifting the resonance curve downward, so that resonance occurs at a lower frequency.
The effect of gradients within a force field on a vibrating cantilever has been described by R. Wiesendanger in Scanning Probe Microscopy and Spectroscopy--Methods and Applications, Cambridge University Press, 1994, on pages 241-243. In such a field, the effective spring constant is given by: ##EQU1##
In the above equation, c is the spring rate of the cantilever in the absence of a force field, and c.sub.eff is the effective spring rate of the cantilever in the presence of the force field. In an attractive force field, with the probe tip being attracted to the surface, the cantilever is effectively softened. In a repulsive force field, with the probe tip being repelled by the surface, the cantilever is effectively stiffened.
The change in the resonant frequency of vibrations of the cantilever/mass system is given by: ##EQU2##
In the above equation, m is an effective mass, and .omega..sub.0 is the resonant frequency of the system in the absence of a force gradient.
In the present example of approaching the surface in a non-contact AC mode, the force gradient is attractive, so the effective spring constant is lowered, lowering the effective natural frequency of the cantilever. As the tip gets closer to the surface, the resonant frequency shifts lower, moving farther from the constant frequency at which the cantilever is driven. This shift in natural frequency significantly decreases the sensitivity of the servo control due to a decrease in the value of the slope (dA/d.omega.) of the curve of vibration amplitude (A) as a function of vibration frequency (.omega.). This decrease in sensitivity reduces the ability of the tip to lock properly in the proximity of the surface during the process of approaching the surface. Often, the tip contacts the surface before it locks at the desired level of engagement. Furthermore, when a strong long range interaction is encountered as the tip approaches the surface, the resonant frequency shifts abruptly, causing a rapid decrease in the amplitude vibrations at the operating frequency. The excitation energy causing the cantilever to vibrate must be significantly increased, sometimes to a level not available from the drive circuits of the instrument, in order to maintain a sufficient level of vibration. This problem is particularly severe when a conventional lock-in circuit is employed for amplitude demodulation, since the amplitude signal from the output of the lock-in demodulator depends not only on the vibration amplitude, but also on the phase angle between the driving signal and the vibration signal. When the resonance shift occurs, the phase angle changes, so that the lock-in output signal decreases much faster than the actual vibration amplitude.
What is needed is a method which can automatically sense the tip to sample surface engagement parameters, such as the degree of engagement and the amount of resonance shift. Such a method is needed for use with the adjustment of system parameters, such as vibration frequency, tip to surface separation, and a level of excitation, in real time, so that the conditions of operation are retained in an optimized state during the process of engaging the sample surface with the probe.
FIG. 1 is a schematic view of conventional apparatus used to determine the amplitude of tip vibration in a scanning force microscope. FIGS. 1A-1C are graphical views of signals in this apparatus. In a scanning force microscope, the signal to be examined, which represents the contour of the sample surface or a force field resulting from electrical or magnetic properties of the sample, is modulated by a vibration signal applied to the probe. Thus, this apparatus is generally called a demodulator.
In the apparatus of FIG. 1, a tip vibration signal 2, shown in FIG. 1A, is applied through a first input line 3, to be multiplied in a mixer 4 by a square wave signal 5, shown in FIG. 1B, applied through a second input line 6. The square wave signal 5 has the same frequency as the vibration tip signal 2, with an amplitude of .+-.1. Since the tip vibration is a result of an excitation signal from an oscillator, the output of the oscillator, having the same frequency, is also used as the square wave signal 5. The resulting intermediate signal 7, shown in FIG. 1C, is fed through a low-pass filter 8 to form a output signal representing the amplitude of the tip vibration signal. In this process, the negative portions of the vibration signal 2 are inverted, being multiplied by (-1), so that both positive and negative portions of the input signal 2 form positive portions of the intermediate signal 7.
A problem with this approach is that the amplitude is properly detected only when the tip vibration signal and the square wave signal are in phase. While the square wave signal 5 is made to match the phase angle of the tip vibration signal 2 with the cantilever vibrating in free space, during the engagement process and during the subsequent process of scanning the surface of the sample, interactions between the vibrating tip and the sample surface cause changes in the phase angle between the signal driving the tip in vibration, and hence the square wave signal 6, and the signal 2 representing measured tip vibration. A variation in phase angle causes portions of the intermediate signal 7 to descend as negative portions, formed by the multiplication of positive portions of the vibration signal 2 by negative portions of the square wave 5, and by the multiplication of negative portions of the vibration signal 2 by positive portions of the square wave 5.
Thus, what is also needed is a method for keeping the square wave signal 6 always in phase with the tip vibration signal 2 during engagement and scanning.